what is the greatest common factor of positive integers j and k?
1)k =j+1
2)jk is divisible by 5.
Answer A?
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GMATGuruNY
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Statement 1: k = j+1Abhijit K wrote:what is the greatest common factor of positive integers j and k?
1)k = j+1
2)jk is divisible by 5.
In other words, j and k are CONSECUTIVE INTEGERS.
Consecutive integers are COPRIMES: they share NO FACTORS OTHER THAN 1.
Thus, the GCF of j and k is 1.
SUFFICIENT.
Statement 2: jk is divisible by 5
If j=1 and k=5, then the GCF of j and k is 1.
If j=5 and k=5, then the GCF of j and k is 5.
Since the GCF can be different values, INSUFFICIENT.
The correct answer is A.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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Hi Abhijit K,
Mitch has pointed out a Number Property that impacts this DS question. Various Number Properties will appear throughout the Quant section on Test Day; they're based on the "little rules" that exist in the realm of math (and in how numbers relate to other numbers). Some of these rules you probably know (for example, what's the product of two odd numbers?......an odd number), while others you'll have to figure out by doing a bit of work.
In this DS question, you might not have noticed the Number Property in Fact 1, but you can still prove that there's a pattern there. EVERY Number Property rule can be proven by TESTing VALUES.
In the prompt, we know that J and K are POSITIVE INTEGERS.
In Fact 1, we're told that K = J + 1
IF....
J = 1
K = 2
The greatest common factor is 1
IF...
J = 2
K = 3
The greatest common factor is 1
IF...
J = 3
K = 4
The greatest common factor is 1
IF....
J = 4
K = 5
The greatest common factor is 1
Etc.
This is clearly a pattern (the answer is ALWAYS 1) and it is enough information to answer the question so Fact 1 is SUFFICIENT. The take-away from this is that you should be prepared to 'play around' with DS questions. Oftentimes the work is really easy, but you have to do enough of it to prove that you have the correct answer.
GMAT assassins aren't born, they're made,
Rich
Mitch has pointed out a Number Property that impacts this DS question. Various Number Properties will appear throughout the Quant section on Test Day; they're based on the "little rules" that exist in the realm of math (and in how numbers relate to other numbers). Some of these rules you probably know (for example, what's the product of two odd numbers?......an odd number), while others you'll have to figure out by doing a bit of work.
In this DS question, you might not have noticed the Number Property in Fact 1, but you can still prove that there's a pattern there. EVERY Number Property rule can be proven by TESTing VALUES.
In the prompt, we know that J and K are POSITIVE INTEGERS.
In Fact 1, we're told that K = J + 1
IF....
J = 1
K = 2
The greatest common factor is 1
IF...
J = 2
K = 3
The greatest common factor is 1
IF...
J = 3
K = 4
The greatest common factor is 1
IF....
J = 4
K = 5
The greatest common factor is 1
Etc.
This is clearly a pattern (the answer is ALWAYS 1) and it is enough information to answer the question so Fact 1 is SUFFICIENT. The take-away from this is that you should be prepared to 'play around' with DS questions. Oftentimes the work is really easy, but you have to do enough of it to prove that you have the correct answer.
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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We can extend the Mitch's and Rich's rules as follows:What is the greatest common factor of positive integers j and k?
1)k = j+1
2)jk is divisible by 5.
If integers J and K differ by n, then the Greatest Common Factor (GCF) of J and K < n
Since statement 1 tells us that integers j and k differ by 1, we can conclude that the GCF of j and j < 1.
Since the GCF cannot be less than 1, the GCF of j and k must equal 1.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
